Vittal Direct Load Control Final Report Part II s16

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Security Enhancement throughDirect Non-Disruptive Load Control

Final Project Report

Part II

Power Systems Engineering Research Center

A National Science FoundationIndustry/University Cooperative Research Center

since 1996

PSERC


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Security Enhancement through Direct

Non-Disruptive Load Control

Final Project Report

Part II

Report Authors

Vijay Vittal, Arizona State UniversityBadri Ramanathan, Iowa State University

PSERC Publication 06-02

January 2006


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Information about this project

For information about this project contact:

Vijay Vittal

Ira A. Fulton Chair ProfessorArizona State UniversityDepartment of Electrical EngineeringTempe, AZ 85287Phone: 480-965-1879Fax: 480-965-0745Email: [email protected]


This is a project report from the Power Systems Engineering Research Center (PSERC).PSERC is a multi-university Center conducting research on challenges facing arestructuring electric power industry and educating the next generation of powerengineers. More information about PSERC can be found at the Centers website:http://www.pserc.org.

For additional information, contact:

Power Systems Engineering Research CenterArizona State UniversityDepartment of Electrical EngineeringTempe, AZ 85287Email: [email protected]

Notice Concerning Copyright Material

PSERC members are given permission to copy without fee all or part of this publicationfor internal use if appropriate attribution is given to this document as the source material.This report is available for downloading from the PSERC website.

2005 Arizona State University. All rights reserved.


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Acknowledgements

The Power Systems Engineering Research Center sponsored the research project titledSecurity Enhancement through Direct Non-Disruptive Load Control. The project began in2002 and was completed in 2005. This is Part II of the final report.

We express our appreciation for the support provided by PSERCs industrial members and by the National Science Foundation under grant NSF EEC-0001880 at Arizona StateUniversity, and NSF EEC-9908690 at Iowa State University, received under the Industry /University Cooperative Research Center program.

The authors thank all PSERC members for their technical advice on the project, especiallyInnocent Kamwa (IREQ), Nicholas Miller (GE Energy), and Sharma Kolluri (Entergy) whoare industry advisors for the project. The authors also acknowledge Dr. Ian Hiskens ofUniversity of Wisconsin, Madison, who contributed technical advice and close cooperationin this work.


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Executive Summary

The transition to a competitive market structure raises significant concerns regarding gridreliability because the grid is being used to support power flows for which it was notdesigned to accommodate. An increase in overall uncertainty in operating conditions makes

generation-based corrective actions at times ineffective leaving the system vulnerable toinstability. The current tools for stability enhancement are mostly corrective and suffer fromlack of robustness to operating condition changes, and they often pose serious inter-areacoordination challenges.

Direct, non-disruptive control of loads has the potential for enhancing preventative control ofoscillatory instability in power systems. The efficacy and robustness of load control wasdemonstrated over a range of operating conditions on different test systems by optimalselection of load types and locations, and of control actions. The research conclusionsconfirm the potential of direct load control for stability enhancement from the perspectives ofcontrol effectiveness, robustness, and potential economic viability. In addition, modern

sensor and communication technologies facilitate use of such geographically-targeted directload control. Thus, loads can be a resource not only for supporting supply adequacy, but alsofor providing essential system reliability services.

The fine control of load for the purpose of damping oscillations may be called loadmodulation. The research covered:

The types of controllable loads;

The fundamental analysis framework and approaches to determine the optimalamount and location of controllable load to achieve the desired damping performancefor the entire power system;

Load modulation requirements to achieve improved system damping in the presenceof uncertainty in load and generation;

Load modulation strategies to control different types of loads so that the desiredstability performance is maintained while causing minimum customer disruption anddiscomfort; and

The effect of various extraneous variables on the effectiveness of load control.

A central problem in using load modulation to maintain stability is determining where andhow much load should be interrupted. To address this problem, a linear model was developedfor identifying optimum load modulation conditions through comprehensive modal analysis.In the model, the controllable load at a bus was modeled as an input to the system to enableanalysis of different load control strategies, and to provide a way to characterize theuncertainty of controllable load levels.

If there is too much uncertainty in the amount of controllable load, load modulation may betoo risky as a strategy for maintaining stability. To examine this issue, robust performanceanalysis was conducted using the linear model. The analysis framework was based on


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Structured Singular Value Theory. Robust performance analysis was used to determine theload levels at particular buses needed for stability control actions that would satisfy thedesired system performance expectations. Two approaches were used to answer thefollowing questions respectively:

1. What is the worst-case uncertainty that would still allow load control to be an

effective strategy (thus meeting operating performance expectations)?2. What is the worst-case damping performance that can be expected given an

uncertainty range?

The first approach used variable load uncertainty bounds; the second approach incorporateduncertainty in load, generation, or in any other system parameter, but with fixed bounds.Both approaches were tested on two reasonably large and complex test systems: CIGRE Nordic and Western Electric Coordinating Council (WECC). The results showed that theload modulation strategies were robustly effective in meeting system stability requirements.

The final part of this research was to develop algorithms for operating controllable thermal

loads air conditioners and water heaters under the proposed load modulation schemes.The algorithms were designed to modulate the loads with minimum disruption or discomfort,while maintaining the desired system stability performance conditions. Two differentalgorithms based on dynamic programming were developed for air conditioner loads. For theair conditioner algorithm, Monte Carlo simulation was used for two different constraintsintroduced in the optimization problem: cycling times and internal temperature excursions. Adecision tree-based algorithm was created for the water heater loads. All of the algorithmsshowed the desired effectiveness in demonstrations on the test systems.

The next steps in developing an implemental load modulation control strategy involve suchresearch issues as:

Techniques to reduce the computation time for load modulation control actions Power system modeling using Prony analysis as an alternative to the component-

based models used in this research

Increased complexity and details in load models

Interaction of load modulation control actions and market decision-making

Communication and information architecture requirements for integration into a state-of-the-art Energy Management System (EMS)

Detailed modeling of stochastic effects such as load forecasting uncertainty within astochastic dynamic programming framework

Multi-agent based computation for direct load control to enable dynamic allocation ofresources


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Table of Contents

1. Introduction..................................................................................................................... 1

1.1 Power System Security ........................................................................................... 1

1.2 Power System Oscillatory Stability ........................................................................ 21.3 Power System Damping Enhancement................................................................... 3

1.4 Load as a Resource ................................................................................................. 4

1.5 Direct Load Control for Security Enhancement ..................................................... 6

1.6 Objectives and Scope of the Research .................................................................. 10

1.7 Test Systems ......................................................................................................... 13

1.7.1 Cigr Nordic (Nordic32) System..................................................................13

1.7.2 Western Electric Coordinating Council (WECC) System............................14

1.8 Outline of the Report ............................................................................................ 16

2. Literature Review.......................................................................................................... 19

2.1 Traditional Load Management in Power Systems................................................ 19

2.1.1 Emergency Load Shedding ...........................................................................19

2.1.2 Direct Load Control ......................................................................................19

2.2 Direct Load Control for Damping Enhancement.................................................. 21

2.3 Robust Control Applied to Power Systems .......................................................... 23

3. Power System Linear Model for Load Control.............................................................25

3.1 Dynamic Equations............................................................................................... 26

3.1.1 Generator Model ...........................................................................................26

3.1.2 Excitation System Model..............................................................................27

3.1.3 Vector of States.............................................................................................29

3.1.4 Overall System Dynamic Equations .............................................................29

3.2 Algebraic Equations.............................................................................................. 31

3.2.1 Vector of Algebraic Variables ......................................................................31

3.2.2 Load Model...................................................................................................313.2.3 Power Balance Equations .............................................................................32


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3.3 Overall System Equation ...................................................................................... 34

3.4 Linearization......................................................................................................... 34

4. Structured Singular Value Based Performance Analysis Framework ..........................38

4.1 Structured Singular Value Theory A Brief Historical Overview ...................... 38

4.2 Uncertainty Representation................................................................................... 39

4.3 Structured Singular Value .................................................................................. 39

4.4 Linear Fractional Transformation......................................................................... 41

4.4.1 Well-posedness of LFTs ...............................................................................42

4.4.2 Definition...................................................................................................... 42

4.4.3 Basic Principle ..............................................................................................42

4.5 Robust Stability..................................................................................................... 44

4.6 Robust Performance.............................................................................................. 45

4.7 Skewed ............................................................................................................... 46

4.8 SSV Based Framework for Robust Performance Analysis ............................... 47

4.8.1 Characterization of Parametric Uncertainty in the Linearized Model ..........47

4.8.2 Characterization of Performance through the Choice of Error Signals ........50

4.8.3 Framework for the Application of Robust Performance Theorem ...............56

5. Skewed Based Robust Performance Analysis for Load Modulation......................60

5.1 Modal Analysis ..................................................................................................... 60

5.1.1 Eigenvalue Sensitivities ................................................................................605.2 Overview of Robust Performance Analysis Approaches ..................................... 62

5.3 Approach I Determination of Worst-case Uncertainty for Fixed Performance. 63

5.3.1 Algorithm for Approach I .............................................................................69

5.3.2 Approach I Numerical Simulations and Results........................................71

5.4 Approach II Determination of Worst-case Performance for Fixed Uncertainty103

5.4.1 Algorithm for Approach II..........................................................................104

5.4.2 Approach II Numerical Simulations and Results.....................................105

6. Load Control Algorithms............................................................................................124

6.1 Background......................................................................................................... 124

6.1.1 Brief Historical Overview of Load Control Technology............................124

6.1.2 Telecommunications Reform Act of 1996..................................................125

6.1.3 Developments in Load Control Systems.....................................................125


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6.1.4 Some Recent Applications of the Above Technologies .............................127

6.2 Air-Conditioner Load Control Optimization Framework................................ 128

6.2.1 Air-Conditioner Load Model ......................................................................128

6.2.2 Basic Setup for the Optimization Problem .................................................129

6.2.3 Dynamic Programming-Based Optimization Objective .............................130

6.2.4 Dynamic Programming-Based Optimization Constraints ..........................130

6.2.5 Dynamic Programming Algorithm Parameters ..........................................131

6.2.6 Assumption of Uncertainties for Monte Carlo Simulations .......................132

6.2.7 Initialization of Scenario.............................................................................132

6.2.8 Small-Signal Stability Performance Boundary...........................................134

6.2.9 Monte Carlo Simulation Results with On/Off Time Constraints................135

6.2.10 Monte Carlo Simulation Results with Constraints on Temperature Excursions.....................................................................................................................150

6.2.11 Qualitative Discussion of Results with Air-Conditioner Control Algorithms.....................................................................................................................161

6.3 Water-Heater Control Optimization Framework ............................................. 162

6.3.1 Model of a Domestic Water-Heater ............................................................162

6.3.2 Cold Load Pickup with Water-Heater Control ...........................................164

6.3.3 Decision Tree-Based Water-Heater Control Algorithm .............................165

6.4 High Level Overview of Direct Load Control Framework ................................ 172

7. Conclusions and Future Work ....................................................................................173

7.1 Conclusions......................................................................................................... 173

7.2 Future Work........................................................................................................ 176


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List of Figures

Figure 1.1 One-line diagram of Cigr Nordic system....................................................... 13

Figure 1.2 One-line diagram of sub-transmission/distribution feeder.............................. 14

Figure 1.3 One-line diagram of WECC system................................................................ 15Figure 3.1 Excitation system model: IEEE AC 4 Type (ETMSP Type 30) .................. 28

Figure 3.2 Excitation system model: IEEE DC 1A Type (ETMSP Type 1) ................. 29

Figure 4.1 Upper linear fractional transformation ............................................................ 42

Figure 4.2 Multiple source of uncertainty ........................................................................ 43

Figure 4.3 Pulling out the s structure ............................................................................ 43

Figure 4.4 RP analysis framework.................................................................................... 44

Figure 4.5 RS analysis framework.................................................................................... 44

Figure 4.6 RP analysis as a special case of structured RS analysis .................................. 46

Figure 4.7 LFT representation of parametric uncertainty in state-space model ............... 49

Figure 4.8 Disturbance input (VREF2) ............................................................................. 52

Figure 4.9 Error signal responses in p.u. for nominal and perturbed plants..................... 53

Figure 4.10 Error signal responses in p.u. for nominal and perturbed plants................... 56

Figure 4.11 Block diagram of the uncertain plant with output......................................... 57

Figure 4.12 State-space model of the system for robust performance analysis................ 58

Figure 4.13 N representation for robust performance analysis .................................... 59

Figure 5.1 State-space model of the uncertain linear model with the performanceweight factored ................................................................................................... 65

Figure 5.2 N representation for robust performance analysis with N

as a function of................................................................................................. 66Figure 5.3 Flowchart of the algorithm for approach I Determination of worst-case

uncertainty for given performance ..................................................................... 70

Figure 5.4 Participating generators and load buses selected for controlin Nordic system................................................................................................. 72

Figure 5.5 Nordic system augmented with sub-transmission/distribution feedersat load buses N51 and N61 at 130 KV level ...................................................... 73

Figure 5.6 Performance bounds for Case 1 (Nordic system)...................................... 75

Figure 5.7 Convergence of performance to unity for Case 1 (Nordic system)........... 76

Figure 5.8 Worst-case performance trade-off curve for Case 1 (Nordic system).......... 77

Figure 5.9 Response of active power output of generator at bus N4072 for a smalldisturbance.......................................................................................................... 78

Figure 5.10 Performance bounds for Case 2 (Nordic system)................................... 79

Figure 5.11 Convergence of performance to unity for Case 2 (Nordic system)......... 80

Figure 5.12 Worst-case performance trade-off curve for Case 2 (Nordic system)........ 81


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List of Figures

(continued)

Figure 5.35 Response of active power generated in MW at bus # 65 for three-phasefault at bus # 44 for different load levels.......................................................... 111

Figure 5.36 Performance bounds for case 2 Approach II (WECC system)............. 112

Figure 5.37 Performance bounds after 3% load modulation for case 2 Approach II(WECC system)................................................................................................ 115

Figure 5.38 Performance bounds with desired performance exactly satisfiedfor case 2 Approach II (WECC system)........................................................ 116


Figure 5.40 Performance bounds for case 3 Approach II (WECC system).............. 118

Figure 5.41 Performance bounds after 10% modulation of loads for case 3 Approach II (WECC system) ........................................................................... 121

Figure 5.42 Performance bounds with desired performance satisfied for case 3 Approach II (WECC system) ........................................................................... 122


Figure 6.1 Screenshot of Carriers Emi thermostat ........................................................ 126

Figure 6.2 Screenshot of HoneywellsExpressStat air-conditioner ............................ 126

Figure 6.3 Basic setup for air-conditioner load control optimization framework .......... 129

Figure 6.4 Dynamic Programming solution parameters ................................................. 133

Figure 6.5 Simulation of internal temperature distributions........................................... 134

Figure 6.6 Assumed variation of ambient temperature................................................... 135Figure 6.7 Desired small-signal stability performance boundary violation with no load

control............................................................................................................... 136

Figure 6.8 Monte Carlo simulation results for maximum off-time 4 min, minimum.. 137

Figure 6.9 Representative perf. boundary violation for maximum off-time 4 min,minimum on-time 2 min................................................................................ 138

Figure 6.10 Monte Carlo simulation results for maximum off-time 2 min,minimum........................................................................................................... 138

Figure 6.11 Representative perf. boundary violation for maximum off-time 2 min,minimum on-time 2 min................................................................................ 139

Figure 6.12 Distribution of internal temperatures at t=200 min with maximumoff-time = 3 min, minimum on-time = 2 min................................................... 140

Figure 6.13 Distribution of internal temperatures at t=200 min with maximumoff-time = 5 min, minimum on-time =2 min .................................................... 140

Figure 6.14 Distribution of internal temperatures at t=200 min with no cycling timeconstraints......................................................................................................... 141


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List of Tables

Table 4.1 Oscillatory modes observed in Nordic system and and participationof different generators ........................................................................................ 51

Table 4.2 Calculated participation factors of speed and angle states for Mode # 7 ......... 51

Table 4.3 Three critical oscillatory modes of WECC system and their participatinggenerators ........................................................................................................... 54

Table 4.4 Calculated Participation factors for speed and angle states.............................. 55

Table 5.1 Eigenvalue sensitivities of active power loads for critical oscillatory mode(Mode 7) for Nordic system ............................................................................... 71

Table 5.2 Nominal and uncertain load levels for case 1 (Nordic system) ..................... 75

Table 5.3 Maximum uncertainty ranges for controllable and total load levelsfor Case 1 (Nordic system).............................................................................. 76







Table 5.10 Significant Eigenvalue sensitivities (real-parts) of load buses for Mode 1 .... 86

Table 5.11 Significant eigenvalue sensitivities (real-parts) of load buses for Mode 2... 86

Table 5.12 Significant eigenvalue sensitivities (real-parts) of load buses for Mode 3..... 87Table 5.13 Nominal and uncertain range for selected loads for case 1

(WECC system).................................................................................................. 88

Table 5.14 Maximum uncertain range for controllable and total load levels for case 1(WECC system).................................................................................................. 91

Table 5.15 Critical modes corresponding to worst-case load levels that satisfy desiredperformance ........................................................................................................ 91

Table 5.16 Nominal and uncertain ranges for new set of selected loads for case 2(WECC system).................................................................................................. 92

Table 5.17 Modified generation levels for case 2 (WECC system) .............................. 93

Table 5.18 Maximum uncertain range for controllable and total load levels for case 2(WECC system).................................................................................................. 95

Table 5.19 Critical modes corresponding to worst-case load levels that satisfy desiredperformance ........................................................................................................ 96

Table 5.20 Modified generation levels for case 3 (WECC system) .............................. 98


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List of Tables

(continued)

Table 5.21 Nominal and uncertain ranges for new set of selected loads for case 3(WECC system).................................................................................................. 98

Table 5.22 Maximum uncertain range for controllable and total load levels for case 3(WECC system)................................................................................................ 101

Table 5.23 Critical modes corresponding to worst-case load levels that satisfy desiredperformance ...................................................................................................... 101

Table 5.24 Uncertainty in generation at bus # 140 and bus # 144 for case 1 Approach II (WECC system) ........................................................................... 106

Table 5.25 Load buses with high eigenvalue sensitivities (real-parts) for Mode 1 ........ 107

Table 5.26 Load modulation levels for case 1 Approach II (WECC system) ............. 108

Table 5.27 Load buses with high eigenvalue sensitivities (real-parts) for Mode 1after load modulation........................................................................................ 109

Table 5.28 Load levels that satisfy chosen performance for case 1 Approach II ........ 110Table 5.29 Uncertainty in generation at bus # 140 and bus # 144 for case 2

Approach II (WECC system) ........................................................................... 111

Table 5.30 Ranking of loads based on eigenvalue sensitivities for mode 1 ................... 113



Table 5.33 Load modulation levels for case 2 Approach II (WECC system) ............. 114

Table 5.34 Load levels that satisfy chosen performance for case 2 Approach II ........ 116

Table 5.35 Critical modes corresponding to worst-case generation levels

in uncertainty range after load modulation....................................................... 117Table 5.36 Uncertainty in generation at bus # 140 and bus # 144 for case 3

Approach II....................................................................................................... 118




Table 5.40 10% Load modulation levels for case 3 Approach II (WECC system)..... 120

Table 5.41 Load levels that exactly satisfy desired performance for case 3 Approach II (WECC system) ........................................................................... 122

Table 5.42 Critical eigenvalues corresponding to worst-case generation levels

after load modulation for case 3 Approach II (WECC system) .................... 123Table 6.1 Usage pattern and water-heater load levels .................................................... 170

Table 6.2 Performance boundary violation with simulated load levels, with andwithout control.................................................................................................. 171


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1. Introduction

Electricity is the most critical energy supply system. It is an indispensable engine of anations economic progress and is the foundation of any prospering society. This profound

value was recently underscored by the United States National Academy of Engineering whenit declared that the vast networks of electrification are the greatest engineering achievementof the 20

thcentury [1]. The role of electric power has grown steadily in both scope and

importance during the last century. In the coming decades, electricity's share of total energyis expected to continue to grow significantly. However, faced with deregulation andincreasing complexity and coupled with interdependencies with other critical infrastructures,the electric power infrastructure is becoming excessively stressed and increasingly vulnerableto system disturbances. For instance, according to the Electric Power Research Institute(EPRI), over the next ten years, demand for electric power in the U.S. is expected to increaseby at least 25% while under the current plans the electric transmission capacity will increaseonly by 4%. This shortage of transfer capability can lead to very serious congestion of the

transmission grids. The process of opening up the transmission system to create competitiveelectricity markets has led to a huge increase in the number of energy transactions over thegrids. Today, power companies are relying on wholesale markets over a wide geographicalarea to meet their demands. Transmission lines built under vertically integrated structureswere not envisioned and designed to transfer power over long distances. These new, heavy,and long-distance power flows pose tremendous challenges to the operation and control ofthe power grid. In addition, the power system infrastructure is highly interconnected andquite vulnerable to physical and cyber disruption. In a vulnerable system, a simple incidentsuch as an equipment failure can lead to cascading events that could cause widespread blackouts. A detailed analysis of large blackouts has shown that they involve cascadingevents in which a rather small triggering failure produces a sequence of secondary failures

that lead to blackout of a large area of the power grid [2, 3, 4, 5].

1.1 Power System Security

The North American Electric Reliability Council (NERC) defines power system security asthe ability of the electric system to withstand sudden disturbances such as electric shortcircuits or unanticipated loss of system elements. Secure operation of electric powerinfrastructure is crucial for a flourishing economy. The cost of major blackouts is immense,in human and financial terms. In a recent study, the total economic cost of the August 2003Northeast blackout has been estimated to be between $7 and $ 10 billion. [6]. There occurnumerous shorter and localized power outages in various areas that have the potential todevelop into major blackouts without timely actions being taken. NERC has published itsfindings on bulk electric system disturbances, demand reductions and unusual occurrencesduring 19792002 [7]. Localized power interruptions and inadequate quality of power causeeconomic losses to the nation, conservatively estimated to be over $100 Billion per year [8].

Reliable and secure operation of power systems is key to the success of deregulation. Withsupply and demand dispersed throughout the system, transmission constraints imposed by


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grid security would result in the capacity available to serve a specific load area being a subsetof the total generation capacity. Under such a scenario, the whole market would getpartitioned into smaller market islands and generation companies within each smaller marketcould then exert market power leading to inefficient outcome or even total collapse ofcompetitive market concept [10, 11]. This kind of scenario has been observed in California

[10], New York and in several other markets around the world [12].

Transmission limitations could occur due to either simple thermal capacity limits of lines ormore subtle system stability limits. Stability limits could be due to either voltage orinsufficient damping for small-disturbance oscillations, and due to large scale transientstability issues. Large power systems exhibit a wide range of dynamic characteristics rangingfrom very slow to very fast dynamics. Disturbances could also be small (e.g., change ofload), large (e.g., loss of a large generator or a load, or a short-circuit on a high-voltagetransmission line or a substation), localized, or widespread. Instability is manifested inseveral different ways depending on the magnitude of the disturbance and its impact as wellas the original operating condition of the system.

1.2 Power System Oscillatory Stability

In recent years, the small-signal oscillatory problem has been one of great concern. Small-signal instability occurs when a system perturbation excites a natural oscillatory mode of thepower system. It deals with the ability of the power system to maintain synchronism underdisturbances that are sufficiently small such that analysis is possible with a linearized modelof the system. In a large power system with many synchronous machines interconnected withloads through transmission lines, several different modes of oscillation exist: local modes,inter-area modes, control modes and torsional modes [13]. Real incidents of small-signalinstability problems have mostly been attributed to inter-area modes. These are lowfrequency oscillations (0.1 Hz 2 Hz) characterized by participation from more than one

machine in the mode and are due to insufficient damping in the system. One classic exampleof this phenomenon is the blackout that happened in the western grid of the U.S in August1996. The mechanism underlying this blackout was the instability caused by growingelectromechanical oscillations (negative damping) due to high power transfers from BritishColumbia to California. Although inter-area oscillatory modes could get excited at any loadlevel, it is generally observed that the more stressed the operating condition of the powersystem is, the more likely it is to lose small-signal stability under small variations in load orgeneration.

In systems where thermal limits are the main constraints, transmission expansion ortransmission upgrade is the only solution for overcoming bottlenecks. However, if stability

limits take precedence over thermal limits, transmission capacity could be improved by eithertransmission expansion through building new lines or by the provision of better stabilitycontrols. Building new lines is more expensive, time-consuming and cumbersome because ofthe need to obtain new rights-of-way and clearances. Additional lines alleviate transmissionconstraints due to thermal limitations and also enhance voltage profile and angular stabilityperformance of the system because they reduce the overall impedance of the network. These


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improvements would only be possible in the short-run with existing generation plants andload levels in the system. However, in the long-run, generating plants will be built andcontracts will be established in such a way that the transmission capacity is used up to themaximum level and the system would again be operating close to the security limits [14].When constraints are imposed due to stability limits, implementing better stability controls is

a less cumbersome choice.1.3 Power System Damping Enhancement

Power System Stabilizers (PSSs) [15] have been the most popular choice for the past twodecades for small-signal stability enhancement. PSSs are continuous feedback-basedcontrollers that add positive damping to generator electro-mechanical oscillations bymodulating the generator excitation. One of the major limitations of conventional PSS is thatof off-line tuning of the parameters in accordance with the operating condition of the system.Conventional PSSs are designed for particular operating points and their parameters need to be adjusted for effective damping at different operating points. A poorly tuned PSS couldresult in a destabilizing effect [13, 16, 17, 18, 19]. Often erratic performance is blamed onpoor PSS tuning, resulting in PSSs being disabled by plant operators and leaving the systemvulnerable to oscillatory instability.

Conventional PSSs are predominantly local controllers on the individual generators, althoughon a theoretical level there has been some research on the use of global signals [20, 21, 22].Use of local controllers to mitigate inter-area oscillations is known to have significantdisadvantages. When multiple PSSs are installed at different machines, coordinating theactions of individual PSS is a serious issue and requires significant analytical andengineering effort. [17, 23, 24, 25]. A detailed study on the impact of interaction amongdifferent power system controls has been undertaken by Cigr Task Force TF 38.02.16.Several incidents of undesirable interactions among PSSs and other controls have been

reported in [23].

Application of speed input or frequency input to PSS in thermal units requires carefulconsideration of the effects of torsional oscillations [17, 27]. The stabilizer, while dampingrotor oscillations can cause instability of torsional modes. In addition, the stabilizer has to becustom-designed for each type of generating unit depending on its torsional characteristics.

In recent years, with the advancements being made in fast power electronic switchingtechnology, power electronics based controls collectively called FACTS (acronym forFlexible Alternating Current Transmission Systems) have generated a lot of interest. Severaldifferent control structures have been proposed for small-signal stability improvement using

FACTS technology [26, 28, 29, 30, 31, 32]. Although these controllers have been shown to be quite effective in damping low frequency oscillations, there are several demeritsassociated with the use of FACTS devices for small-signal stability enhancement.

One of the major demerits is the overall cost of installing the technology. The totalinvestment cost for a single FACTS device of several 100 MVArs could be in the order of


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tens of millions of dollars. Although FACTS devices are still cheaper than building newtransmission lines, the overall cost of installing FACTS based controllers is massive. It iseconomically prohibitive to install FACTS devices only for small-signal stability performance. In fact, in some cases a carefully designed and properly tuned PSS has beenshown to give a better damping performance compared to FACTS controllers [31]. Unless

carefully designed and coordinated, most FACTS controllers offer only limited transientstability improvement. FACTS controllers have also been shown to have limitations withrespect to robustness to system operating conditions [28, 30, 33, 34].

FACTS controllers need to be carefully coordinated among themselves as well as with other power system controls, especially excitation systems and PSSs if any. If not properlycoordinated, FACTS based controls could adversely interact and cause instability [12, 23, 31,35]. Independently designed FACTS controllers operating in the same electrical area have been shown to have destabilizing control interaction [12, 23, 36, 37]. It is extremelyimportant to perform a coordinated design among all FACTS devices.

From the above discussion, it is clear that the small-signal stability enhancement controlmeasures currently in place fall short of robustness requirements. They present seriouscoordination challenges. They are often disabled when such careful coordination cannot beperformed, leaving the system vulnerable to disturbances. FACTS based schemes are highlycapital intensive. With deregulation, there have also been ownership and responsibility issueswith respect to these controls that are discussed in Section 1.5. Robust non-capital intensivestability enhancement schemes that pose no complex coordination issues would be highlydesirable.

Control of active power loads for small-signal stability enhancement, as has been explainedin Section 1.5, is inherently robust. Direct non-disruptive control of selected active powerloads, if designed to be implemented with the existing distribution automation infrastructure,is highly cost effective. Although careful coordination of controllable loads is highlydesirable for improved performance, lack of coordination would not result in seriouslydeteriorating performance. Market-based operation of loads, as detailed in Section 1.4,resolves ownership and responsibility issues related to security enhancement. With theavailability of enabling technologies and an increased interest in demand side resources,direct non-disruptive control of loads is a very promising strategy for stability enhancement.

1.4 Load as a Resource

Load management programs in vertically integrated power systems have existed for manyyears. Section 2 in this report describes in detail these well-established practices with respect

to load management in power systems. Utilities have in the past resorted to load shedding aswell as interruptible load management for power system reliability only under extremeconditions. This practice was partly due to NERCs definition of reliability. It encompassestwo concepts: adequacy and security. Adequacy standards require that there be sufficientgeneration to meet the projected needs plus reserves for contingencies. Security standardsrequire action by system operators to ensure that the system will remain intact even after


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outages or other equipment failures occur. The traditional vertically integrated utilitymanaged short-term reliability by dispatching its own generation. In competitive electricitymarkets, system operators responsible for maintaining reliability own no generation and mustestablish markets for reliability services. This change in the industry structure and theassociated emergence of wholesale energy and reliability markets create new opportunities

for demand-side resources. Under deregulation, the scope of load management programs hasconsiderably broadened.

With the emergence of deregulation, there have been tremendous developments in enablingtechnologies especially with respect to two-way communication, load control systems,monitoring, and metering. Todays technology enables communication and control of severaldistributed resources almost in real-time and has been a major factor in the recent interest indemand-side resources. It is technically feasible for many distributed loads to simultaneouslyreceive customized control signals.

Load management programs are called demand response programs under deregulation and

are designed and operated by the Independent System Operators (ISOs) or the RegionalTransmission Operators (RTOs); they bring several new participants into the market such asretail suppliers, aggregators, curtailment service providers, etc. In 2002, the United StatesSupreme Court validated the authority of Federal Energy Regulatory Commission (FERC)over wholesale transmission sales and enabled the commission to dictate rules forcompetitive energy markets. Subsequently, in the same year, FERC proposed StandardMarket Design (SMD) a single set of market rules that would eliminate the differences between regional electricity markets and thereby standardize the U.S. energy market [38].SMD is perhaps the most important step towards harnessing the benefits of competitiveelectricity markets and was developed by gathering best practices around the U.S. throughan exhaustive stakeholder process. According to SMD, demand response is an importanttenet in standardizing energy markets. SMD provides an appropriate platform for integrationof demand response into the wholesale market structure [39]. In SMD, FERC stronglyadvocates demand participation on an equal footing with generation resources in order toachieve effective competitive performance in electricity markets [38, 39]. In fact, a loadserving entity (LSE)s ability to cut back on power use (i.e., demand response) when calledby an ISO or an RTO will be considered equivalent to supply [38, 39, 40, 41]. This wholenew perspective towards treating load as a system resource has sparked intense interest in therole for demand response in the efficient and reliable operation of deregulated power systems[42, 43, 44, 45, 46, 47, 48, 49, 50].

Demand response in the context of SMD is defined as load response called for by others and price response managed by end-use customers [51]. Load response includes direct loadcontrol, partial as well as complete load interruptions. Price response includes real-timepricing, dynamic pricing, coincident peak pricing, demand bidding and buyback programs.Demand response could be classified into two broad categories: market-based and reliability- based [52]. Market-based demand response programs enable efficient interaction of supplyand demand for price stability. One of the earliest well-known works in the area of market- based control of loads was done by F.C. Schweppe et al [53]. Reliability-based demand


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standards at minimum cost. However, in deregulated systems, the decision-making is highlydecentralized. The Independent Power Producers (IPPs) make investment decisions in thegeneration segment based on the current market conditions as well as forecasts, amongseveral other factors. IPPs also make the decision as to the type of generation to invest in. Inrecent years, there has been rapid progress in combustion turbine technology. Natural gas

fired combined cycle plants constitute the large majority of additions that are continuing to be made in the generation sector. Their response characteristics differ substantially fromconventional steam or hydro-turbine generating units [64, 65]. The primary objective ofpower producers in a deregulated system is control and optimization of their own resources.System reliability services, such as active reserves/frequency control, reactivereserves/voltage control and stability control are only secondary objectives. For example, useof higher cost generators with improved excitation systems and PSS would not be normallyadopted by IPPs without hard rules to define compensation of associated costs involved.From the viewpoint of transient stability, IPPs may not be willing to participate in special protection schemes for the same reason and this may jeopardize system reliability. Alsoinformation exchange for modeling and analysis are more complicated in a market

environment. The IPP could consider having no obligation to inform the others on what isoccurring to its plant. It may not have adequate data acquisition capabilities. Thiswithholding of information, either intentional or otherwise, could be detrimental to overallsystem reliability [Ch. 8 of 67]. The responsibility of system reliability and stability restswith the independent system operator, which although powerful does not own the resourcesthat are necessary to ensure the availability of the above services. There is a need for a clearframework for the allocation of security costs to entities not contributing their share ofreliability services.

Setting aside ownership and responsibility issues, the associated technical problems related tostability themselves are potentially more complex in a restructured power system [66]. Thiscan be attributed to several factors. Notable among these are an increase in the amount,geographical scope as well as frequency of changes in power flows, increased utilization oftransmission, and the operation of the system closer to its limits. There is a strong need foreffective, robust and adaptive control solutions in a deregulated system.

The advancements in some of the enabling technologies for the demand-side brieflydiscussed in the previous section and detailed in Section 5 open up several new directions forpower system stability enhancement and control. These advancements could be put to use indeveloping innovative, cost-effective solutions for stability enhancement, that make the bestutilization of the existing infrastructure while not requiring major capital investments.Established competitive market frameworks have been developed or are in the stages of thedevelopment for demand side participation in related reliability resources such as active power reserves. With a clear preference by FERC for market-based solutions for theprocurement of reliability services, control schemes for stability enhancement that make useof such competitive frameworks for load participation are attractive. Such market-basedschemes enable resolution of issues related to the allocation of security costs. From a systemreliability standpoint, customers could be viewed as willing to sell excess of reliability to the


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e) Minimal cost: Loads are not specifically designed to respond to power system needs.It is desirable that adding additional capabilities for the load is not costly.

The control strategy, the dynamic performance improvement possible through load control,and the amount and type of disruption caused to the customer depend on the type of the load

being controlled.

Under deregulation, there is a strong need to possess tools and techniques for securityassessment that produce operating limit boundaries for both static and dynamic security of power systems. Knowledge of such operating limits a priori would enable the systemoperator to efficiently procure services that are necessary to operate the system securely.Besides, an increase in overall uncertainty in operating conditions makes corrective actions attimes ineffective, leaving the system vulnerable. Tools and techniques currently available forstability enhancement are mostly corrective in nature, and lack robustness to operatingcondition changes, as discussed in the previous sections.

The approach developed in this research is based on preventive control of distributed loads inorder to improve system dynamic performance. Based on the desirable characteristics ofloads for control applications as mentioned above, the following loads have been selected ascontrollable: residential and commercial air conditioner/heating loads and water-heater loads.

Direct load control for stability enhancement is based on the fundamental premise that thecumulative effect of controlling several individually insignificant loads distributedgeographically and electrically, provides sufficient leverage for the system to be operatedsecurely at times when the system is vulnerable. By selecting loads to be controlledappropriately and by optimizing the time duration for control action for each load, it is possible to accomplish secure operation while minimizing the amount of disruption to thecustomer. The control strategy involved in activating load control will have significant bearing on the overall system reliability. The type of load to be controlled and theperformance improvement that could be obtained greatly influence the control strategy. Non-critical loads could be controlled selectively, leaving critical loads uninterrupted.

As a comparison, a power system stabilizer modulates excitation, thereby the reactive powergenerated, to effect a change in the terminal bus voltage which in turn affects the nearbyvoltage dependent loads as well as power transfer. These two effects could be of comparablemagnitude [34]. Depending on the system operating condition, they could be additive orcould counteract each other. The net impact of this modulation is thus unpredictable and to alarge extent depends on operating conditions. An SVC operates in the same way. On theother hand, control of active power loads is a direct way of controlling power flows. Hencethe scheme is inherently robust. In a practical power system, the number of dominantoscillatory modes is often larger than the number of control devices available to controlthem. The robustness with regard to direct load control implies that it is conceptually possible to damp out different inter-area modes that get excited at different power flowlevels.


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In modulating loads with appropriately designed algorithms, much of the existinginfrastructure for demand side management could be made use of. Control of loads at thedistribution level would not require new installations at the high voltage level. The additionalinvestment needed in most cases would not be massive.

1.6

Objectives and Scope of the Research

This research proposes robust oscillatory stability enhancement through cost-effective, direct,non-disruptive control of loads. The control strategy for load control is preventive in nature.

The objective of this research is to address the following broad issues with respect to controlof loads:

The type of loads to be controlled A fundamental analysis of the framework and different approaches based on the

framework to decide on optimal location and amount of load to be controlled, in orderto achieve a desired damping performance for the entire power system

Modulation of loads to achieve improved system damping in the presence ofuncertainty in loads as well as in generation

Strategies used to control different loads so that the desired stability performance ismaintained in the system while causing minimum disruption

The effect of various extraneous variables on the effectiveness of load control.

The underlying framework for analysis to determine the optimal amount of load to bemodulated is based on the Structured Singular Value (SSV or) theory. The SSV theory inrobust control [119, 121] offers a powerful technique to analyze robustness as well as designcontrollers that satisfy robust performance for linear control systems with uncertainties thatcan be represented in a structured form. It has previously been successfully applied in

analyzing stability robustness [132, 133] of power systems and in designing robust PSS andSVC damping controllers [134, 135]. In this research, the setup for uncertaintycharacterization in power systems developed in [132] has been extended to develop a robustperformance analysis framework. Robust performance analysis deals with the determinationof maximum uncertainty bounds for which the system satisfies desired performancespecifications. Robust performance analysis is performed through the application of therobust performance theorem [122].

The scope of this research work includes the following:

1. Development of a linear model for the problem of direct load control. This linearmodel would serve as the basis for the analysis framework. It would also be appliedin selecting the optimal locations for load modulation through a comprehensivemodal analysis. The important difference between a linear model for direct loadcontrol and those used in other power system control designs is the fact that the loadavailable for control at a bus is modeled as an input to the system. This allows the useof different load models for controllable load at each load bus and is essential tocharacterize the uncertainty in the controllable part of the load.


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2. The linear model developed for direct load control is cast into a framework suitable

for the application of the robust performance theorem, one of the fundamentaltheorems related to SSV concept. The uncertainty in the operating conditions in termsof load levels or generation is real-parametric uncertainty and could be represented in

a structured form thereby making it possible for SSV-based analysis. A frameworkfor robust performance analysis is developed from a Linear Fractional Transformation(LFT) representation of uncertainty in the state-space model and the dampingperformance specifications in terms of the MIMOH norm.

3. The objective of robust performance analysis is to determine load levels at busesselected for control implementation, which would satisfy the desired performancespecifications. Depending upon the uncertainty characterization as well as the robust performance analysis problem formulation, there are two fundamentally differentapproaches to an analysis of the above problem.

(a) Determination of worst-case uncertainty for a given performance specification In this formulation of the problem, active power load at each load bus selectedfor control is assumed to be the sum of controllable and uncontrollable parts.Uncertainty is assumed to exist in the controllable part of the loads. The analysisthen proceeds to determine the maximum uncertainty range for the controllableas well as the total load levels that satisfies the damping performancespecifications. It has been analytically shown that with the above uncertaintycharacterization and the criterion for performance specification satisfied, it isalways possible to determine the maximum uncertainty range in load levels thatwould satisfy the chosen performance conditions.

(b) Determination of worst-case performance for a given uncertainty range Thisapproach, in principle, is similar to NASAs patented on-line method for robustflutter prediction for air-craft models [145]. This is a fairly general formulationof the problem and it allows uncertainty to exist not only in load levels, but ingeneration levels as well as in any parameter of the system. However, theuncertainty bounds are assumed to be fixed. To start with, for the givenuncertainty range, the worst-case performance is computed. If it does not satisfythe desired specifications, the algorithm modulates the load levels at selectedload buses in the system. The load modulation is iterative and is performed untilthe load level in the system is such that the chosen performance specificationsare satisfied for the uncertainty range under consideration. The selection of loadbuses for control implementation is based on the eigenvalue sensitivity of activepower loads.

Both the above formulations are skewed formulations in the context of SSVtheory [144]. The first approach is applied with variable load uncertainty bounds andthe second approach is applied with uncertainty in load, generation, or in any othersystem parameter, however, with fixed bounds.


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In the determination of load levels that satisfy the chosen damping performanceconditions, the analysis could be done at the transmission level of the system. Theamount of load to be modulated at the transmission level could then be dividedamongst multiple feeders that connect at the transmission level load bus.

Alternatively, the system at transmission voltage level could be augmented with sub-transmission and distribution systems and the determination of the amount of load to be modulated could be done at the distribution level. Both these approaches havebeen illustrated.

4. Develop algorithms for operating controllable thermal loads air conditioners andwater heaters based on the results of the analysis problem described above. Incontrolling the group of thermostatically driven loads, the phenomenon of cold loadpickup needs to be modeled and taken care of. Also, control needs to be distributedamong several groups of loads available for control. The objective is to operate theloads with minimum disruption or discomfort, while maintaining the load levels such

that the desired performance conditions are satisfied. Two different algorithms basedon Dynamic Programming with different sets of constraints are proposed for air-conditioner loads, while a decision-tree based algorithm is proposed for water-heaterloads. The development of these algorithms is in line with some of the most recentload management programs executed.


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The numerical data for the Cigr Nordic test system is available in [141]. This systemrepresents the interconnected Nordic and Swedish power system and has dynamic propertiessimilar to these systems. It consists of 20 generators and 41 buses. There are 14 load busesavailable for control. The nineteen 400 kV transmission system buses in Figure 1.1 are givenbus numbers starting with 4. Similarly the two 220 kV buses and the eleven 130 kV buses of

the transmission system have numbers starting with 2 and 1 respectively. Nine load buses at130 kV level have two digit numbers and are connected to the 400 kV network throughtransformers with tap changers.

In this research, the Nordic test system is extended to sub-transmission and distributionvoltage levels. This is done by augmenting the system with multiple number of sub-transmission/distribution feeders connected to transmission level load buses selected forcontrol. The sub-transmission/distribution feeders have been designed specifically for thisresearch using the data available in [142]. The design details are provided in Appendix A.Figure 1.2 shows the one-line diagram of the sub-transmission/distribution feeder along withthe voltage levels.

Figure 1.2 One-line diagram of sub-transmission/distribution feeder

The Nordic system augmented with feeders of the configuration shown in Figure 1.2 isreferred to as the augmented Nordic system henceforth.

1.7.2 Western Electric Coordinating Council (WECC) System

The second test system employed in this research is a reduced model of the westerninterconnection of the U.S. electric power system. This system has 29 generators and 179buses at 230 kV, 345 kV and 500 kV voltage levels. The one-line diagram of the system isshown on Figure 1.3. In Figure 1.3, the buses are numbered from 2 to 180.

130/46.5 KV

Line 1Length=20 mi

13 KVLine 2Length=8 mi

46.5/13 KV

130 KV


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.

Figure 1.3 One-line diagram of WECC system


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1.8 Outline of the Report

This report consists of 7 sections. Section 1 provides the background and motivation as wellas an introduction to the problem. The objectives and scope of this research have beendescribed in detail. The test systems used in this research have been introduced along with

their one-line diagrams.

Section 2 provides a detailed summary of the literature review undertaken for this research.The relevant literature has been segregated and discussed as shown below:

Section 2.1 reviews literature related to traditional load management in powersystems. This section consists of two sub-sections. Within the broader topic oftraditional load management, literature related to emergency load shedding has beendiscussed in section 2.1.1 and that related to direct load control had been discussed inSection 2.1.2. Literature on direct load control has been segregated further anddiscussed in Sections 2.1.2.1 and 2.1.2.2. Section 2.1.1.1 discusses literature relatedto cold load pickup and physically based modeling of loads. Section 2.1.1.2 discusses

literature on stochastic aggregation of loads. Section 2.2 reviews literature on direct load control applied for damping

enhancement. Section 2.3 reviews literature on the application of robust control techniques in power

system control design and analysis.

Section 3 presents a detailed derivation of the state-space linear model of the power systemfor the problem of load control. It has been organized as follows:

Section 3.1 provides a description of the mathematical models of power systemcomponents and dynamic equations corresponding to the models.

Section 3.2 presents the algebraic equations for the purpose of deriving the linear

model. Section 3.3 presents the differential algebraic set of the overall system equations. Section 3.4 presents the step-by-step linearization procedure and the linear model

derived.

Section 4 deals with the development of an analysis framework for load modulation based onstructured singular value theory. The necessary mathematical concepts have been presentedin detail followed by the development of the analysis framework. This section is organized asfollows:

Section 4.1 presents a brief historical overview of the development of structuredsingular value theory in the area of robust control.

Section 4.2 discusses different ways of characterizing uncertainty in physical systems.The uncertainty characterization and its basis for the problem at hand have also beenbriefly discussed.

Section 4.3 discusses in detail the concept of structured singular value. The definitionof structured singular value and the necessary background have been presented.

Section 4.4 discusses linear fractional transformation (LFT), an important concept


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related to performing analysis and design for robust control. The problem of well- posedness of LFTs, formal definition of LFT, and the basic principle behind theapplication of LFTs have been discussed in sub-sections 4.4.1, 4.4.2 and 4.4.3respectively.

Section 4.5 discusses robust stability and a theorem on robust stability.

Section 4.6 discusses robust performance and a theorem on robust performance. Section 4.7 discusses the concept of skewed and its relevance to the loadmodulation analysis approaches presented later in Section 5.

Section 4.8 presents a description of the development of SSV-based analysisframework for robust performance. It has been organized into the following sub-sections: Section 4.8.1 provides a detailed treatment of the characterization of parametric

uncertainty in the state-space model of the power system developed in Section 3.The different sources of parametric uncertainty have been presented followed bythe representation of uncertainty in LFT form.

Section 4.8.2 deals with characterization of small-signal stability performance in

the analysis framework through the choice of appropriate error signals.Simulation results with the linear simulation tool, SIMGUI, available in Matlab toolbox for the augmented Nordic system and the WECC system have beenpresented in sub-sections 4.8.2.1.1 and 4.8.2.1.2.

Section 4.8.3 presents the development of the analysis framework through theapplication of parametric uncertainty and performance characterizations.

Section 5 deals with two different skewed based robust performance analysis approachesfor load modulation that are based on the framework developed in Section 4. This section hasbeen organized as follows:

Section 5.1 presents a detailed description of modal analysis using eigenvalue

sensitivities for the selection of appropriate locations for load modulation. Section 5.2 provides a comprehensive overview of the robust performance analysisapproaches proposed in this section. The basis for the two different approachesdeveloped as well the conceptual difference between the two approaches has beenclearly outlined. The relevance of the robust performance analysis problem to theconcept of skewed and its implications have also been discussed.

Section 5.3 deals with approach I for load modulation analysis determination ofworst-case uncertainty for fixed performance. The basic assumptions andfundamental aspects related to this approach and the analytical background have all been explained in detail. In addition, an analytical proof of the correctness of theapproach has been presented. Section 5.3.1 presents the algorithm for approach I.

Numerical and simulation results for approach I on the augmented Nordic system andthe WECC system have been presented in Section 5.3.2. Section 5.4 provides a detailed treatment of approach II for load modulation analysis

determination of worst-case performance for fixed uncertainty. The algorithm forapproach II has been described in Section 5.4.1. Numerical and simulation results forapproach II have been presented for the WECC system in Section 5.4.2.


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Section 6 deals in detail with different specialized algorithms developed for real-timemodulation of loads. This section consists of the following four parts:

Section 6.1 presents a detailed overview of the background for the load modulationalgorithms proposed in this section. A brief historical overview of load controltechnology, recent developments in load control systems as well as some recent

applications of the above technologies in different utilities in the U.S. have beendescribed. Section 6.2 provides a description of the optimization framework developed to study

air-conditioner load control. The air-conditioner load model, the basic setup assumedfor the optimization problem, and the dynamic programming based optimizationproblem have all been explained in detail. The basis for Monte Carlo simulation andthe uncertainties assumed in performing Monte Carlo simulation have also beenexplained. Monte Carlo simulation results have been provided with two differenttypes of constraints introduced in the optimization problem, constraint on cyclingtimes, constraint on internal temperature excursions. The impact of constraints as wellas various parameters and variables have been studied in these results. A qualitative

discussion of the results with the different DP algorithms has also been provided. Section 6.3 describes the development of an optimization framework to study thecontrol of water-heaters. The model of a domestic water-heater assumed for this workhas been explained followed by a decision-tree based control algorithm developedthrough the application of the model. Two different approaches to arrive at the datarequired for implementing the algorithm have also been dealt with. The algorithm hasbeen illustrated with a numerical result.

Section 6.4 provides a high-level overview of the direct load control framework basedon the algorithms proposed in this section.

Section 7 provides a summary of specific contributions of this research as well as suggestions

for future work.


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proposed in order to optimize the amount of load management with different objectives.Dynamic programming based approaches have been quite popular [80, 82, 83, 84]. Fuzzylogic and linear programming based algorithms have also been proposed [76, 85, 86]. Adetailed treatment of these algorithms has been provided in Section 5 of this report. There isa variety of economic as well as reliability issues that will have to be taken into consideration

in formulating a load management strategy. These issues are utility-specific. The usualpractice is to assess in detail several multiple strategies and then choose the most economicalstrategy or a combination of strategies [77].

2.1.2.1 Cold Load Pickup and Physically based Modeling of Loads

The usual types of loads controlled in load management programs have been thermostaticallydriven loads such as air-conditioners and space-heating and water-heater loads. In someschemes for provision of contingency reserves, control of municipal water-pumping loadshas been proposed [87]. Due to the stochastic nature of thermostatic loads, it is essential tostudy the load dynamic response during and after control periods in order to assess theimpact of a load management program on power system performance. When an aggregate ofthermostatically driven loads is switched off, there occurs a surge in the total load when theyare switched back to service [88]. This phenomenon is called cold load pickup and isessentially the result of loss of diversity among thermostatically driven loads. This was firstidentified as a potential problem in 1949 when Audlin et alpresented the results of a stagedoutage in Syracuse, New York [89]. It is one of the most studied aspects in distributionsystem design and analysis.

In order to take into account the effect of cold load pickup in a load management study, theload equipments will have to be modeled accurately by physically based models. Suchmodels capture the physics of operation of the equipments and predict the response to controlactions. Several physical models have been proposed for studying cold load pickup in both

air-conditioners and water-heaters . In one of the earliest attempts, Galiana et al [90] proposed an empirical method for predicting physical load. This method lacks amathematical formulation. It is not suitable for short-term load prediction, but could be usedfor long-term load management. In 1981, Ihara and Schweppe [91] presented a dynamicmodel for the temperature of a house that is heated by a thermostatically driven heater. Thismodel is fairly simple and has been proven to capture the behavior of thermal loadsaccurately. Several refinements of this model are available in the literature. In [92], thismodel has been converted into a sample-data form by discretizing time and has been used tostudy the aggregate load behavior. Actual utility data is examined and it has been identifiedthat the recovery transient has two epochs. Five different heating load models with differentcharacteristics to model the two epochs have been studied. Reference [93] suggests the

development of a residential load model based on physically based simulation. Reference[94] proposes a lumped parameter model of an air-conditioner with the parametersdetermined through system identification techniques such the as maximum likelihoodprinciple. In [95], the thermodynamic behavior of a house is modeled using a parallel RCcircuit. Door openings and other small heat flows are modeled as a random current source inthe circuit. A stochastic model for heating and cooling loads is presented in [96]. This model


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includes the random influences in the environment through the introduction of discrete whitenoise term. It is used to study the effect of stochastic characteristics of different parameters ofthe model developed in [91]. Reference [97] presents a detailed model for air-conditioningloads by capturing weather effects more accurately. The effects of humidity and solarradiation in the model for air-conditioning are represented in [98]. Reference [99] suggests

the importance of modeling the stochastic aspects of lifestyles in the development ofphysically-based load models.

References [100, 101, 102, 104] present different physically-based models of electric water-heating loads. Development of water-heater models is based on water-heater usage pattern aswell as the physics of water-heating. Reference [103] simulates actual control scenariosthrough the application of the model developed in [100]. It has been shown that [100]captures the response to control actions quite accurately.

2.1.2.2 Stochastic Aggregation

With individual equipments modeled in sufficient detail, the behavior of a group of suchloads could be studied through simulation. However, there have also been several stochastictechniques proposed to aggregate individual thermostatically driven loads. Reference [104] presents stochastic aggregation of a group of water-heater loads. The resulting model is atraveling wave model. In [94], with the assumption that the switching processes areergodic, the mean duty factor as well as the sample variance of duty factor for a group of air-conditioner loads are calculated using Kalman Filter expressions. The aggregate model isfurther applied to study energy consumption, voltage response etc. Reference [97] developsan aggregate model of a group of air-conditioners based on an analogy between lumpedparameter heat flow problems and lumped parameter electric circuits. It has been shown toclosely model the aggregate demand as well as energy payback effect after an outage. In[95], aggregate dynamics for a homogenous group of devices are derived as a set of Focker-

Planck equations system of coupled ordinary partial differential equations. A perturbationanalysis yields the dynamics for a non-homogenous group.

2.2 Direct Load Control for Damping Enhancement

Power system small-signal stability improvement through the control of active power loadswas suggested as early as in 1968 by R.H. Park [111]. However, this concept was notinvestigated closely until the mid 90s, possibly because of a lack of enabling technologies.Damping of electro-mechanical oscillations through the control of active power loads wasfirst studied in detail in [112]. References [113, 114, 115, 116] are based on [112]. Withrespect to the application of direct load control for stability enhancement, [112] examines

modal analysis for the selection of load buses for control implementation, selection ofappropriate feedback signals for the load controller that capture the poor dampingcharacteristics, type of load controller for load modulation, controller design and practicalconsiderations in implementing direct load control for oscillatory stability enhancement. Theentire power system with all component models is represented by a time-invariant differentialalgebraic system of equations (DAE). Selection of the best location for implementing loadcontrol is based on both the active power controllability as well as eigenvalue sensitivity for


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3. Power System Linear Model for Load Control

The tools and techniques of modern robust control, including the Structured Singular Valuetheory, are all applicable to linear control systems. The foundation for analysis and design

using these techniques is a linear model of the uncertain control system. The linear modeltogether with proper uncertainty characterization is expressed in a form suitable for theapplication of robust control techniques. In this section the linear model suitable forapplication of Structured Singular Value based robust performance analysis for the directload control problem is derived.

The following approach is adopted to build a linear model of the power system for the loadcontrol problem: Each individual component in the system is modeled in sufficient detailwith its dynamic model. These individual dynamic models are coupled together through thenetwork algebraic equations using a common reference [139]. Linearizing the systeminvolves eliminating the algebraic variables corresponding to the network, resulting in a

linear model that relates the derivative of the states with the states and the inputs.

The linear model developed in this section for the load control problem is different fromother linear models used in power system control design. The difference is that, in the modeldevelopment, the total active power load at certain candidate load buses is assumed to be thesum of controllable and uncontrollable parts. The controllable parts of the load at such loadbuses are then modeled as system inputs. This facilitates the following:

i) Characterization of uncertainty in the controllable parts of the loads for thedevelopment of analysis framework

ii) Calculation of eigenvalue sensitivity and active power controllability for loadinputs, which are used in the selection of optimal locations for load modulation

iii) The use of different load models for the controllable and uncontrollable parts of theload.

The functional notation of the differential algebraic system of equations that describe thepower system is as follows:

U)Y,G(X,0

U)Y,F(X,X

=

=&(3.1)

where X and Y are the vectors of state variables and algebraic variables, respectively; F andG are functions ofX and Y.

Linearizing the above set of equations around an operating point,

UU

FY

Y

FX

X

FX

+

+

=& (3.2)

UU

GY

Y

GX

X

G0

+

+

= (3.3)


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From (3.3)

UU

G1

Y

GX

X

G1

Y

GY

= (3.4)

Substituting forY in (3.2) yields

UU

G1

Y

G

U

FX

X

G1

Y

G

X

FX

+

=& (3.5)

= UBXA + (3.6)

3.1 Dynamic Equations

3.1.1 Generator Model

3.1.1.1 Two-axis Model

In this research, generators have been modeled by the two-axis model [139]. The two-axismodel for a generator accounts for the transient effects in flux, while the sub-transient effectsare neglected. The transient effects are dominated by the rotor circuits, which are the fieldcircuit in the direct (d) axis and an equivalent circuit in the quadrature (q) axis formed by thesolid rotor. Following are the two key assumptions made in this model:

i. In general, the stator voltage generated is the sum of two parts: speed voltage part and

the part corresponding to the rate of change of flux. The two-axis model makes theassumption that the part corresponding to the variation of flux-linkages of d- and q-axes is negligible compared to the speed voltage part.

ii. 1= S

The dynamic equations corresponding to the two-axis model are given by:

( ) iiiiii qqqddq IxxEE += &0 (3.7)

( ) iiiiiii dddqFDqd IxxEEE += &0 (3.8)

)(DI)Ix(x)EIE(IPMsiidqqqqqddmi iiiiiiiiii ++=

(3.9)sii =& (3.10)

i=1,2,,Ng

where

A


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:, qdEE d-axis and q-axis stator EMFs corresponding to rotor transient flux components,respectively

Id,Iq: d-axis and q-axis stator currents

:00, qd open-circuit direct and quadrature axes transient time-constants

:, ddxx direct axis synchronous and transient reactances

:, qq xx quadrature axis synchronous and transient reactances

EFD: stator EMF corresponding to f

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